Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x-9y &= 6 \\ -5x-4y &= -7\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-5x = 4y-7$ Divide both sides by $-5$ to isolate $x$ $x = {-\dfrac{4}{5}y + \dfrac{7}{5}}$ Substitute this expression for $x$ in the first equation. $-4({-\dfrac{4}{5}y + \dfrac{7}{5}}) - 9y = 6$ $\dfrac{16}{5}y - \dfrac{28}{5} - 9y = 6$ Simplify by combining terms, then solve for $y$ $-\dfrac{29}{5}y - \dfrac{28}{5} = 6$ $-\dfrac{29}{5}y = \dfrac{58}{5}$ $y = -2$ Substitute $-2$ for $y$ in the top equation. $-4x-9( -2) = 6$ $-4x+18 = 6$ $-4x = -12$ $x = 3$ The solution is $\enspace x = 3, \enspace y = -2$.